English

Hyperbolic (1,2)-knots in S^3 with crosscap number two and tunnel number one

Geometric Topology 2008-12-17 v1

Abstract

A knot in S^3 is said to have crosscap number two if it bounds a once-punctured Klein bottle but not a Moebius band. In this paper we give a method of constructing crosscap number two hyperbolic (1,2)-knots with tunnel number one which are neither 2-bridge nor (1,1)-knots. An explicit infinite family of such knots is discussed in detail.

Keywords

Cite

@article{arxiv.0812.3086,
  title  = {Hyperbolic (1,2)-knots in S^3 with crosscap number two and tunnel number one},
  author = {Luis G. Valdez-Sanchez and Enrique Ramirez-Losada},
  journal= {arXiv preprint arXiv:0812.3086},
  year   = {2008}
}

Comments

31 pages, 11 figures. To appear in Topology and its Applications (2008)